To express diverse natural phenomena such as sound, heat, electrostatics, elasticity, thermodynamics, fluid dynamics, and quantum mechanics mathematically, various partial differential equations (PDEs) have been derived and numerical methods can be applied to solve these PDEs. Representative numerical methods for solving PDEs are the finite difference method, finite element method, finite volume method, spectral method, etc. We focus on the finite difference method (FDM) which is to divide a given domain into finite grids and find an approximate solution using derivatives with finite differences [1]}. This method uses each and its neighbor points to predict the corresponding point at the next time step. Likewise, in convolutional neural networks (CNNs) [2]}, convolution operators extract each pixel of an output by using the corresponding pixel and its neighbor pixels of an input. Also, the convolution operator is basically immutable. Hence, well-structured convolutional neural networks have a potential to solve partial differential equations numerically. Therefore, we propose Five-point stencil CNN (FCNN) containing a five-point stencil kernel and a trainable approximation function to obtain numerical solutions of the PDEs. Among the various PDEs representing natural phenomena, we deal with reaction-diffusion type equations. The reaction-diffusion model has been applied and used in various fields such as biology [3]}, [4]}, [5]}, chemistry [6]}, [7]}, [8]}, image segmentation [9]}, [10]}, [11]}, image inpainting [12]}, [13]}, [14]}, medical [15]}, [16]}, [17]}, and so on. In this paper, we use second order reaction-diffusion type equations: heat, Fisher's, Allen–Cahn (AC) equation, and reaction-diffusion equations with trigonometric functions terms.
